Removal-sampling family

Sequential-depletion removal sampling: latent abundance N_i ~ Poisson(lambda_i) (or negative binomial) observed through K ordered removal passes, where pass k removes Binomial(N_i - sum_{l<k} y_{il}, p_{ik}) of the individuals still present. The declining catch sequence identifies detection p and abundance N; the latent N is summed out in closed form (truncation K_max), so the fit is a direct Laplace approximation (no EM), with a NUTS path over the same marginal.

Usage

removal(K_max = NULL, mixture = c("poisson", "negbin"))

Arguments

K_max

upper bound for the latent-abundance marginal sum (the exact integration over N is truncated at K_max). NULL (default) lets the engine pick max(y) + 100 (matching unmarked::pcount()); raise it if a fit warns that the posterior over N puts mass on the boundary.

mixture

latent-abundance distribution, both fitted via tulpa's closed-form marginal Laplace engine. "poisson" is the default; "negbin" (negative binomial, Var(N) = lambda + lambda^2 / r) adds an overdispersion parameter r. Non-spatially the log size log_r is estimated jointly with the coefficients and reported with an SE; on the areal-spatial path (method = "nested_laplace") r is integrated over the outer hyperparameter grid and reported as a posterior mean / sd. Named mixture (after unmarked::pcount()) to avoid collision with the model-type family argument of tobs().

Value

A tobs_family object.

Details

The tobs() formula is the abundance (log lambda) model; detection is the per-pass detection (logit p) model. The response y is an n_sites x K integer matrix of per-pass removals with the passes in column order; complete pass sequences are required (no NA).

References

Royle, J. A. (2004). N-mixture models for estimating population size from spatially replicated counts. Biometrics 60, 108-115. Dorazio, R. M., Jelks, H. L., Jordan, F. (2005). Improving removal-based estimates of abundance. Biometrics 61, 1093-1101.

Examples

f <- removal(K_max = 100)
f